In a typical gauge R&R experiment, each operator () makes multiple observations on each of several similar parts () from a monitored process. The statistical model used to describe the response variable is the balanced two-factor crossed random model with interaction

where is an unknown constant, and are jointly independent normal random variables with means of zero and variances and , respectively. The corresponding SAS statements are as follows:

   proc varcomp method=grr;
      class P O;
      model y = P|O;
   run;

The first random effect in the MODEL statement is assumed to be the "Part" effect and the second is "Operator."

The ANOVA table for the preceding model is shown in Table 94.1.

The gauge R&R parameters of interest are given in Table 94.2 in terms of and

For a one-way model, and for a two-way model with no interaction,

If you use the SPECLIMITS option to give specification limits, the two parameters in Table 94.3 will also be estimated and displayed.

Here, USL and LSL are the specification limits, and the value corresponds to the number of standard deviations between the "natural" tolerance limits of a normal process.

If you use the RATIO option, the ratios in Table 94.4 will also be estimated and displayed.